Linking individual and collective contests through noise level and sharing rules

Abstract

We propose the use of Nitzan’s (1991) sharing rule in collective contests as a tractable way of modelling individual contests. This proposal (i) tractably introduces noise in Tullock contests when no closed form solution in pure strategies exists, (ii) satisfies the important property of homogeneity of degree zero, (iii) can be effort or noise equivalent to a standard Tullock contest

Technological Change, Campaign Spending and Polarization

“…9 The campaign stage for impressionable voters is resolved via Tullock's ratio-form CSF that facilitates the comparative statics of our model. In the symmetric case, our results would have the same qualitative features if we considered the difference-form CSF proposed by Alcalde and Dahm (2007), the tractable noise CSF proposed by Amegashie (2006) or the relative-difference CSF by Beviá and Corchón (2015) under the parameter restrictions proposed by Balart, Chowdhury, and Troumpounis (2017). and impressionable with ex-ante probability 1 − F (y).…”

Heterogeneity, Leveling the Playing Field, and Affirmative Action in Contests

“…The parameter r is often interpreted as the returns to scale from effort (Perez-Castrillo and Verdier, 1992; Baye, Kovenock, and De Vries, 1994;Nti, 1999): r > 1 indicating increasing returns and r < 1 indicating decreasing returns. We interpret r as the noise in the CSF (Amegashie, 2006;Jia, 2008;Balart, Chowdhury, and Troumpounis, 2017). Setting r = 0 implies that the contest outcome is completely random and independent of individual effort levels; when r = 1, the contest takes the form of a raffle or lottery, and when r = ∞, an all-pay auction is staged.…”

Heterogeneity, leveling the playing field, and affirmative action in contests

“…The parameter r is often interpreted as the returns to scale from effort (Baye et al, 1994;Nti, 1999;Perez-Castrillo & Verdier, 1992): r > 1 indicating increasing returns and r < 1 denoting decreasing returns. Alternatively, r is interpreted as the noise in the CSF (Amegashie, 2006;Balart et al, 2017;Jia, 2008) and this is the interpretation we follow. Setting r = 0 implies that the contest outcome is completely random and independent of individual effort levels; when r = 1, the contest takes the form of a raffle or lottery (L), and when r ¼ ∞, it characterizes an APA.…”

“…The parameter r is often interpreted as the returns to scale from effort (Perez-Castrillo and Verdier, 1992;Baye, Kovenock, and De Vries, 1994;Nti, 1999): r > 1 indicating increasing returns and r < 1 indicating decreasing returns. We interpret r as the noise in the CSF (Amegashie, 2006;Jia, 2008;Balart, Chowdhury, and Troumpounis, 2017). Setting r = 0 implies that the contest outcome is completely random and independent of individual effort levels; when r = 1, the contest takes the form of a raffle or lottery, and when r = ∞, an all-pay auction is staged.…”